I have had success with an Attiny84 using its internal oscillator with my customised version of optiboot installed on it, and then disabling its reset pin. I can then use UART to upload new programs.

The process should work for the Attiny85 also.

If you download this core:https://github.com/TCWORLD/ATTinyCore/

Then in the IDE, select "Optiboot Attiny85 @8MHz", and then using ISP, burn the bootloader using the IDE.

Then connect the attiny to a serial port (you can use an arduino board with its processor removed). PB1 is the Tiny RX pin, PB0 is the Tiny TX pin.

If you open the serial monitor at 9600 board, then unplug power for the Attiny and reconnect it again (to reset it), it should print stuff to the serial monitor. If you can't read it dont worry, just keep sending the letter 'x' (lower case) with no line ending. Each time it will print something to the serial monitor. Eventually (maybe 10 to 15 times of sending 'x') it will stop printing stuff. At this point the bootloader is ready and the internal oscillator is calibrated.

You should then be able to upload sketches via the serial port. Once you have confirmed that you can do that, you will need to use avrdude to set the fuses to disable the reset pin making sure not to erase the chip.